Crystalline solids entropy

To melt ice we have to put heat into the system. This increases the system entropy via eqn. (5.20). Physically, entropy represents disorder and eqn. (5.20) tells us that water is more disordered than ice. We would expect this anyway because the atoms in a liquid are arranged much more chaotically than they are in a crystalline solid. When water freezes, of course, heat leaves the system and the entropy decreases. 

In electrochemistry it is customary to multiply each of those quantities by Avogadro s constant and, when a few additional ions enter the already saturated solution, to speak of the entropy of solution per mole. Let the entropy of one mole of the crystalline solid be denoted by Scr and let Si and S2 denote, respectively, the entropy of the solution before, and after, the entry of the additional solute, both expressed in calories per mole. The total initial entropy is obviously (S + Si) and the final entropy is St. The difference between the final and the initial entropy is by definition AS,at. 

The heat of solution of silver bromide in water at 25°C is 20,150 cal/mole. Taking the value of the entropy and the solubility of the crystalline solid from Tables 44 and 33, find by the method of Secs. 48 and 49 the difference between the unitary part of the partial inolal entropy of the bromide ion Br and that of the iodide ion I-. 

These effects are shown in Figure 17.4, where the entropy of ammonia, NH3> is plotted versus temperature. Note that the entropy of solid ammonia at 0 K is zero. This reflects the fact that molecules are completely ordered in the solid state at this temperature there is no randomness whatsoever. More generally, the third law of thermodynamics tells us that a completely ordered pure crystalline solid has an entropy of zero at 0 K. 

Third law of thermodynamics A natural law that states that the entropy of a perfectly ordered, pure crystalline solid is 0 at 0 K Thomson, J. J., 25 Three Mile Island, 525-526 Threonine, 622t Tin... 

Supercooled liquids (glasses111) also have residual entropy at 0 Kelvin. As an example, glycerol supercools badly so that a glass is usually obtained at a low temperature. A crystalline solid can also be obtained if the liquid is cooled in a certain manner to initiate crystalization. Gibson and Giauque9 started with... 

This is an expression of Nernst s postulate which may be stated as the entropy change in a reaction at absolute zero is zero. The above relationships were established on the basis of measurements on reactions involving completely ordered crystalline substances only. Extending Nernst s result, Planck stated that the entropy, S0, of any perfectly ordered crystalline substance at absolute zero should be zero. This is the statement of the third law of thermodynamics. The third law, therefore, provides a means of calculating the absolute value of the entropy of a substance at any temperature. The statement of the third law is confined to pure crystalline solids simply because it has been observed that entropies of solutions and supercooled liquids do not approach a value of zero on being cooled. 

The relationship among heat capacity, entropy, and temperature in crystalline solids may be understood on the basis of two fundamental concepts the Boltzmann factor and the partition function (or summation over the states, from the German term Zustandsumme). Consider a system in which energy levels Eq,... 

As shown by Helgeson et al. (1978), satisfactory estimates of standard state molar entropy for crystalline solids can be obtained through reversible exchange reactions involving the compound of interest and an isostructural solid (as for heat capacity, but with a volume correction). Consider the generalized exchange reaction... 

Third Law of Thermodynamics. Also referred to as the Nernst heat theorem, this law states that it is impossible to reduce the temperature of any system, via a finite set of operations, to absolute zero. For any changes involving perfectly crystalline solids at absolute zero, the change in total entropy is zero (thus, A5qk = 0). A corollary to this statement is that every substance, at T > 0 K, must have a positive and finite entropy value. The entropy of that substance is zero only at absolute zero when that substance is in pure, perfect crystalline form. See Entropy... 

Some pure substances from a glass-like solid, on cooling, rather than a crystalline solid. In such solids the molecules have a certain randomness in their spatial distribution, more like a liquid than a crystal. This is an example in which a metastable state rather than an equilibrium state is obtained on cooling. If such a solid is obtained on cooling to the lowest experimental temperature, then the value of the entropy function at 0 K, obtained on extrapolation, will be greater than zero. 

In contrast to AfG° and Afl° which are relative values (representing differences between values for the compound and the elemental reference states, arbitrarily assigned to be zero), standard entropy values, S° (Frame 16, section 16.2) are absolute values. This arises because the entropy of a perfectly crystalline solid at the absolute zero of temperature has a value of zero (Frames 16 and 17), i.e. ... 

Since we also know that a crystalline solid is more ordered than the corresponding liquid which, in turn, is more ordered than the corresponding vapour phase, then since entropy is related to degree of disorder (Boltzmann equation (17.1), Frame 17) then ... 

Studies related to entropy changes revealed that reduction in temperature leads to decrease in entropy change for all processes. It was therefore, postulated that for a process occurring at absolute zero temperature the entropy change would be zero. This has led to a basis from which absolute values of entropy can be determined, taking entropy at absolute zero of temperature to be zero. Thus, unlike i/and F whose changes can be accurately measured but not the absolute value, the absolute value of entropy can indeed be measured. We take, for calculation purposes, enthalpy of elements in a defined standard state to be zero, but that assumption is only for convenience, no molecule or atom can have zero heat content at ambient conditions. On the other hand, a fully ordered (crystalline) solid at absolute zero temperature will have zero entropy. 

This increase in entropy is because of the order lost when a crystalline solid dissociates to form ions. 

Figure 15-14 (a) A simplified representation of a side view of a perfect crystal of a polar substance of 0 K. Note the perfect alignment of the dipoles in all molecules in a perfect crystal. This causes its entropy to be zero at 0 K. There are no perfect crystals, however, because even the purest substances that scientists have prepared are contaminated by traces of impurities that occupy a few of the positions in the crystal stracmre. Additionally, there are some vacancies in the crystal structures of even very highly purified substances such as those used in semiconductors (see Section 13-17). (b) A simplified representation of the same perfect crystal at a temperature above 0 K. Vibrations of the individual molecules within the crystal cause some dipoles to be oriented in directions other than those in a perfect arrangement. The entropy of such a crystalline solid is greater than zero, because there is disorder in the crystal. 

At zero Kelvin (0 K), there is no energy available for a chemical to sample states. The absolute entropy, S, of a pure crystalline solid at 0 K is zero. Absolute entropy may be measured and calculated for different substances at different temperatures. 

Under ideal conditions, Fig. 2.5 shows a phase diagram between a supersaturated crystalline solid solution, the glassy state, and the liquid. At the triple point, the entropy of fusion vanishes and melting becomes a glass transition. The crystalline phase is strictly unstable beyond this composition (at any temperature). If this argument is valid, then any solid-state process which drives the... 

Moreover, the equation can only be accurate for small strains, since considerable change in the end-to-end distance of the cords would distort the Gaussian distribution of statistical chain elements. This happens more readily for a smaller value of It also implies that at increasing strain, the chemical bonds in the primary chain become increasingly distorted. Consequently, the increase in elastic free energy is due not merely to a decrease in conformational entropy but also to an increase in bond enthalpy. If the value of is quite small, even a small strain will cause an increase in enthalpy. (In a crystalline solid, only the increase in bond enthalpy contributes to the elastic modulus.)... 

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